计及非齐次边界条件的面内变速运动黏弹性板的稳态响应

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摘要研究非齐次边界条件和1∶3内共振下面内平动黏弹性板的横向非线性1∶2主参数振动的稳态响应。考虑黏弹性对边界条件的影响，建立了面内平动板的偏微分运动方程和相应的非齐次边界条件。采用直接多尺度法建立了次谐波参数共振时的可解性条件，并根据Routh-Hurvitz判据判别了系统幅频响应的稳定性。讨论了速度扰动幅值和黏弹性系数对幅频响应的影响，对比了齐次和非齐次边界条件下稳态响应的差异。最后，引入微分求积法验证直接多尺度法的近似解析结果。

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关键词 ：面内运动板, 次谐波参数振动, 1∶3内共振, 多尺度方法, 微分求积法

Abstract：Steady-state responses for lateral nonlinear 1∶2 principal parametric resonance of a viscoelastic plate with in plane 1∶3 internal resonance of translation were investigated under nonhomogeneous boundary conditions. A governing partial differential equation of motion and corresponding nonhomogeneous boundary conditions for the plate with in plane translation were established considering effects of viscoelasticity on boundary conditions. The multi-scale method was applied to establish the solvability conditions during the plate having sub-harmonic parametric resonance. The stability of the system’s frequency-amplitude responses was judged using Routh-Hurvitz criterion. Effects of in-plane translation speed disturbance amplitude and viscoelastic coefficient on the system’s steady-state responses were investigated. The system’s steady-state responses under homogeneous boundary conditions and non-homogeneous ones were compared. Finally, the differential quadrature method was introduced to verify approximate analytical results using the multi-scale method.

Key words： plate with in plane motion sub-harmonic parametric resonance 1∶3 internal resonance multi-scale method differential quadrature method

收稿日期: 2019-01-17 出版日期: 2020-06-28

引用本文:

张登博1，陈立群1,2. 计及非齐次边界条件的面内变速运动黏弹性板的稳态响应[J]. 振动与冲击, 2020, 39(13): 156-162.
ZHANG Dengbo1， CHEN Liqun1,2. Steady-state responses of a viscoelastic plate with in plane variable speed motion under non-homogeneous boundary conditions. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(13): 156-162.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I13/156

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